Andrea Sacchetti

insegnamenti

Meccanica Razionale e Statistica

Orario di ricevimento

Si riceve per appuntamento tramite posta elettronica.

Profilo biografico

Laureato a Modena nel 1987 in Matematica. Dal 1988 al 1991 sono stato borsista presso l’Istituto Nazionale di Alta Matematica ed insegnante di Informatica Industriale presso l’I.T.I. “L. da Vinci” di Carpi. Dal 1991 al 1999 sono stato ricercatore in Fisica Matematica presso la Facoltà di Scienze MM, FF e NN dell’Università di Modena, dal 1999 al 2001 sono stato Professore Associato di Meccanica Razionale presso la Facoltà di Ingegneria dell’Università di Modena, infine dal 2001 sono Professore Ordinario di Fisica Matematica presso la Facoltà di Scienze MM, FF e NN dell’Università di Modena. Sono stato Presidente del Consiglio di Corso di Laurea in Matematica e  membro del Senato Accademico dell’Università di Modena e Reggio Emilia. Sono membro del Comitato Scientifico del Gruppo Nazionale per la Fisica Matematica.

Aree di interesse

Metodi matematici per la meccanica quantistica

Pubblicazioni

Research Articles

• 1. Bentosela F, Caliceti E, Grecchi V, Maioli M, Sacchetti A, Analyticity and asymptotics for the Stark-Wannier states, J. Phys. A: Math. and Gen. 21 (1988), 3321-3331.
• 2. Grecchi V, Sacchetti A, Weak-field magnetic bands in superlattices and the single-band approximation, J. Phys. A: Math. and Gen. 22 (1989), 4989-5006.
• 3. Maioli M, Sacchetti A, One-dimensional many point interactions and stability of eigenvalues, Bolettino U.M.I. (7) 5-A (1991),363-372.
• 4. Grecchi V, Maioli M, Sacchetti A, Horn of singularities for the Stark-Wannier ladders, J. Phys. A: Math. and Gen. 24 (1991), 4275-4282.
• 5. Sacchetti A, Asymptotic expansion of the Stark-Wannier states, Helv. Phys. Acta 65 (1992), 11-31.
• 6. Maioli M, Sacchetti A, Strong asymptotic expansion for the exponential anharmonic oscillator, Atti Sem. Mat. Fis. Univ. Modena XL (1992), 25-30.
• 7. Grecchi V, Maioli M, Sacchetti A, Stark resonances in disordered systems, Commun. Math. Phys. 146 (1992), 231-240.
• 8. Grecchi V, Maioli M, Sacchetti A, Wannier ladders and perturbation theory, J. Phys. A: Math. and Gen. 26 (1993), L379-L384.
• 9. Barbieri M, Maioli M, Sacchetti A, Singular continuous spectrum in a class of random Schroedinger operators, Appl. Math. Lett. 6 (1993), 23-26.
• 10. Grecchi V, Maioli M, Sacchetti A, Stark ladders of resonances: Wannier ladders and perturbation theory, Commun. Math. Phys. 159 (1994) 605-618.
• 11. Grecchi V, Sacchetti A, Asymptotics of Zener double-well splittings and magnetic gaps, J. Phys. A: Math. and Gen. 27 (1994), 1393-1399.
• 12. Maioli M, Sacchetti A, Absence of absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentials, J. Phys. A: Math. and Gen. 28 (1995), 1101-1106.
• 13. Grecchi V, Sacchetti A, Crossing and anticrossing of resonances: the Wannier-Stark ladders, Annals of Physics 240 (1995),258-284.
• 14. Grecchi V, Martinez M, Sacchetti A, Double well Stark effect: crossing and anticrossing of resonances, Asympt. Anal. 13 (1996), 373-391.
• 15. Grecchi V, Martinez M, Sacchetti A, Splitting instability: the unstable double wells, J. Phys. A: Math. and Gen. 29 (1996), 4561-4587.
• 16. Grecchi V, Sacchetti A, Lifetime of the Wannier-Stark resonances and perturbation theory, Commun. Math. Phys. 185 (1997), 359-378.
• 17. Grecchi V, Sacchetti A, Metastable Bloch oscillators, Phys. Rev. Lett. 78 (1997), 4474-4477.
• 18. Sacchetti A, Band functions for the Lame’ equations, MapleTech 4 (1997), 28-33.
• 19. Grecchi V, Sacchetti A, Wannier-Bloch oscillators, Comm. Math. Phys. 197 (1998), 553-569.
• 20. Maioli M, Sacchetti A, Erratum --- Absence of absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentials, J. Phys. A: Math. and Gen. 31 (1998), 1115-1119.
• 21. Losi A, Sacchetti A, First-kind Fredholm integral equations with kernel of Hankel type, Inverse Problems 15 (1999), 281-290.
• 22. Grecchi V, Sacchetti A, Molecular localization induced by collisions, Phys. Rev. A 61 (2000), 2106-2109.
• 23. Grecchi V, Sacchetti A, Critical metastability and destruction of the splitting in non-autonomous systems, J. Stat. Phys. 103 (2001), 339-368.
• 24. Grecchi V, Sacchetti A, The acceleration theorem for Bloch oscillators, Phys. Rev. B 21 (2001), 2303-2307.
• 25. Sacchetti A, Dynamical localization criterion for driver two-level systems, J. Phys. A: Math. And Gen. 34 (2001), 10293-10306.
• 26. Grecchi V, Martinez A, Sacchetti A, Destruction of the beating effect for a non-linear Schroedinger equation, Comm. Math. Phys. 227 (2002), 191-209.
• 27. Sacchetti A, Instability of the tunnelling distruction effect in a quasi-periodically driven two-level system, Europ. Phys. J. D 21 (2002), 229-232.
• 28. Sacchetti A, Nonlinear time-dependent one-dimensional Schrodinger equation with double-well potential, SIAM J. Math. Anal. 35 (2003), 1160-1176.
• 29. Maioli M, Sacchetti A, Gevrey formal power series of Wannier-Stark ladders, J. Phys. A: Math. And Gen. 37 (2004), 2371-2383.
• 30. Grecchi V, Sacchetti A, Critical conditions for a stable molecular structure, J. Phys. A: Math. and Gen. 37 (2004), 3527-3534.
• 31. Sacchetti A, Nonlinear time-dependent Schroedinger equations: the Gross-Pitaevskii equation with double-well potential, J. Evol. Eq. 4, (2004), 345-369.
• 32. Sacchetti A., Nonlinear double-well Schrodinger equations in the semiclassical limit, J. Stat. Phys. 119, (2005) 1347-1382.
• 33. Maioli M, Sacchetti A., Two level systems driven by a stochastic perturbation, J. Stat. Phys. 119, (2005) 1383-1396.
• 34. Lodi D., Maioli M., Sacchetti A., Dynamical localization for two-level systems periodically driven, J. Phys. A: Math. And Gen. 38, (2005). L23-L30.
• 35. Adami R., Sacchetti A., The transition from diffusion to blow-up for a nonlinear Schrodinger equation in dimension 1, J. Phys. A: Math. And Gen. 38, (2005). 8379-8392.
• 36. Della Casa F.F.G, Sacchetti A.. Stationary states for non linear one-dimensional Schrodinger equations with singular potential, Physica D, 219, (2006), 60-68.
• 37. Bambusi D., Sacchetti A., Exponential times in the one-dimensional gross-pitaevskii equation with multiple well potential, Comm. Math. Phys. 275, (2007), 1-36.
• 38. Bambusi D., Sacchetti A., Stability of spectral eigenspaces in nonlinear Schrodinger equations, Dynamics of PDE 4, (2007), 129-141.
• 39. Kovarik H., Sacchetti A., Resonances in twisted quantum waveguides, J. Phys. A: Math. and Gen. 40, (2007), 8371-8384.
• 40. Sacchetti A., Spectral splitting method for nonlinear Schroedinger equations with singular potential, J. Comp. Phys. 227, (2007), 1483-1499.
• 41. Sacchetti A., Effective mass approximation with non-parabolic bands, J. Phys. Soc. Japan 77, (2008).
• 42. Sacchetti A., Bloch oscillators in a slowly perturbed external field, J. Phys. A: Math. and Gen. 41, (2008), 265304.
• 43. Sacchetti A., Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential, Phys. Rev. Lett. 103 (2009), 194101.
• 44. Kovarik H., Sacchetti A., A nonlinear Schrodinger equation with two symmetric point interactions in one dimension, J. Phys. A: Math. and Gen. 43 (2010), 155205
• 45. Sacchetti A., Hysteresis effects in Bose-Einstein condensates, Phys. Rev. A 82 (2010) 013636.
• 46. Sacchetti A., Electrical current in nanoelectronic devices, Phys. Lett. A 374, (2010), 4057-4060.
• 47. Cuoghi G., Bertoni A. and Sacchetti A., Effect of quasibound states on coherent electron transport in twisted nanowires Phys Rev B 83 (2011) 245439
• 48. Grecchi V., Kovarik H., Martinez A., Sacchetti A., Sordoni V., Resonant states for a three-body problem under an external field, Asympt. Anal. (2011) – in press
• 49. Fukuizumi R., Sacchetti A., Bifurcation and stability for nonlinear Schrodinger equation with double well potential in the semiclassical limit, arxiv:1104.1511v1, submitted (2011).
  
  Conference Proceedings
  
  
• 1. Grecchi V, Maioli M, Sacchetti A, Stark ladders and perturbation theory in Mathematical Results in Quantum Mechanics (ed. Demuth M), Operator Theory: Advances and Applications 70, Birkhauser Verlag (Berlin) (1994) 33-36.
• 2. Sacchetti A, Destruction of the beating effect in a periodically driven double well, Proceedings of the International Conference APTEX, Bologna 13--17.9.1999 (ed. Graffi S and Martinez A).
• 3. Sacchetti A, Tunneling destruction for a non-linear Schroedinger equation, Proceedings of the International Conference Q-Math 8: Mathematical results in Quantum Mechanics, Taxco (Mex) 10-14.12.2001 (ed. Exner P and Weder R).
  
  Contribution to Books
  
  
• 1. Sacchetti A., Perturbation Theory, semiclassical, Chapter of the Encyclopedia of Complexity and Systems Science (Ed. Springer Verlag: 2008).
• 2. Adami R.,Noja D., Sacchetti A., On the mathematical description of the effective behaviour of one-dimensional Bose-Einstein condensates with defects, chapter in the book Bose-Einstein Condensates: Theory, Characteristics, and Current Research, (ed. Nova Publisher: 2010).